|y + 4| < 1
(1 point)
- 5 < y < - 3
O - 3 < y < 5
O - 4 < y < 1
O 1 < y < 4
- 3 < y < - 5
To solve the inequality |y + 4| < 1, we need to consider two cases: when y + 4 is positive (y + 4 > 0) and when y + 4 is negative (y + 4 < 0).
Case 1: y + 4 > 0
If y + 4 is positive, then the inequality becomes y + 4 < 1, which simplifies to y < -3.
Case 2: y + 4 < 0
If y + 4 is negative, then the inequality becomes -(y + 4) < 1, which simplifies to -y - 4 < 1. Adding 4 to both sides, we get -y < 5. Multiplying by -1 (and reversing the inequality sign), we have y > -5.
Combining both cases, we have -5 < y < -3.
Therefore, the correct answer is: -5 < y < -3.
To solve the inequality |y + 4| < 1, we need to consider two cases: when y + 4 is positive and when y + 4 is negative.
1. When y + 4 is positive:
In this case, the absolute value can be removed, and the inequality becomes y + 4 < 1. Solving for y, we subtract 4 from both sides of the inequality:
y + 4 - 4 < 1 - 4
y < -3
2. When y + 4 is negative:
In this case, the absolute value can also be removed, and the inequality becomes -(y + 4) < 1. To remove the negative sign, we multiply both sides of the inequality by -1. Keep in mind that when we multiply an inequality by a negative number, the direction of the inequality flips:
-1 * -(y + 4) > -1 * 1
y + 4 > -1
y > -1 - 4
y > -5
Thus, the solution for the original inequality |y + 4| < 1 is -5 < y < -3.